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R. H. Hardin , Sep 25 2013
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Number of defective 3-colorings of an nX3 n X 3 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
Empirical: a(n) = 12*a(n-1) - 36*a(n-2) for n>3.
Conjectures from Colin Barker, Jun 16 2017: (Start)
G.f.: 48*x^2*(1 - 2*x) / (1 - 6*x)^2.
a(n) = 2^(2+n)*3^(n-2)*(2*n - 1) for n>1.
(End)
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R. H. Hardin, <a href="/A229505/b229505.txt">Table of n, a(n) for n = 1..210</a>
allocated for R. H. Hardin
Number of defective 3-colorings of an nX3 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order
0, 48, 480, 4032, 31104, 228096, 1617408, 11197440, 76142592, 510603264, 3386105856, 22251552768, 145118822400, 940369969152, 6060162023424, 38868625391616, 248257671856128, 1579821548175360, 10020582391283712
1,2
Column 3 of A229510
Empirical: a(n) = 12*a(n-1) -36*a(n-2) for n>3
Some solutions for n=4
..0..0..1....0..1..2....0..1..1....0..1..0....0..1..2....0..1..0....0..1..0
..2..2..2....2..1..2....2..2..0....0..2..0....0..1..0....2..2..2....2..1..2
..0..1..1....0..1..0....0..1..1....1..1..0....1..1..2....1..0..0....1..0..2
..1..2..0....1..2..2....2..2..1....0..2..1....0..0..2....1..2..0....2..0..1
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R. H. Hardin Sep 25 2013
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allocated for R. H. Hardin
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